Crews were called to the vicinity of Hillcrest Street near Nelson Avenue just after 7 a.m.
The vehicle ran off the road and struck a house, damaging a vehicle parked in the driveway.
Homeowner John Bon said he and his wife were not hurt when the truck crashed into their bedroom wall.
One person sustained a serious injury, authorities said. The driver was able to remove himself from the vehicle, according to police.
FDNY officials said the driver suffered a medical episode from an unknown condition. Witnesses said he was conscious when he was taken to the hospital.
The Department of Buildings has been called to assess the structural damage; the truck was towed away Wednesday morning. Inspectors determined the truck impacted the front of the single-story home, damaging masonry brick and dislodging structural wood framing.
Despite the damage, DOB engineers found that the building is structurally stable, according to the department. A partial vacate order was issued, affecting the home's front yard and bedroom.
Fuel coming from the box truck was seen spilling along the street, and FDNY crews were working to contain the spill.
AIR11 was over the scene, where firefighters were seen surrounding the Peapod grocery delivery truck and assessing the damage.
Stop & Shop, a corporate sibling of Peapod, confirmed it was their truck in the crash following the driver's emergency.